Phi-array: A novel method for fitness visualization and decision making in evolutionary design optimization

The class of genetic algorithms (Gas) is a member of the evolutionary algorithms (EAs). In Gas, a solution is considered as a phenotype and the chromosome representation is a genotype. In a canonical GA, the genotypic search space could be tightly coupled with the phenotypic solution space under a specific encoding scheme. Variants of the canonical Gas are developed based on how the problem is represented in both the genotypic space and phenotypic space. This paper focuses on Gas that utilizes both genotypic and phenotypic spaces and investigates some of the effects of the coupling of the two spaces.

Approximate models have to be used in evolutionary optimization when the original fitness function is computationally very expensive. Unfortunately, the convergence property of the evolutionary algorithm is unclear when an approximate model is used for fitness evaluation because approximation errors are involved in the model. What is worse, the approximate model may introduce false optima that lead the evolutionary algorithm to a wrong solution. To address this problem, individual and generation based evolution control are introduced to ensure that the evolutionary algorithm using approximate fitness functions will converge correctly. A framework for managing approximate models in generation-based evolution control is proposed. This framework is well suited for parallel evolutionary optimization in which evaluation of the fitness function is time-consuming. Simulations on two benchmark problems and one example of aerodynamic design optimization demonstrate that the proposed algorithm is able to achieve a correct solution as well as a significantly reduced computation time.

Challenging multi-modal optimization problems have been very successfully solved by evolutionary computation (EC) techniques. To date, many methods have been proposed on evolutionary optimization for both single and multiobjective large scale problems. In the age of Big Data, there is an urge to take evolutionary optimization techniques to the next level for solving problems with even larger scales: thousands and millions of variables. These problems arise in many domains ranging from bioinformatics, to neuroscience and social simulations. In this paper, we investigate the use of EC to solve Big electroencephalography (EEG) data optimization problems with thousands of variables. The optimization problem attempts to identify maximum information that should be kept from a signal while minimizing the artifact. The high level of epistasis inherent in a signal can slow down the evolution. Therefore, we investigate the advantages of optimizing the problem in the frequency domain with different thresholds as opposed to the time domain. We propose synthetic EEG data sets of various scale and noise level. These data sets were the basis for the Optimization of Big Data 2015 Competition (BigOpt), CEC 2015. Two state-of-art multiobjective evolutionary algorithms (MOEAs) were evaluated. The results of this work suggest that frequency representation of the signals facilitates dimensionality reduction for big scale optimization of time series data, and hence provides faster and better quality solutions for EEG data cleaning. Moreover, the results suggest that existing state-of-art multiobjective evolutionary computation methods are extremely slow. Methods that can optimize the problem faster and with high quality are needed.

Although various optimization methods for solving single-objective problems have been developed in the last few decades, these methods have lost their eligibility due to the fact that today’s engineering problems are toward multiple objective optimization problems, in real applications. For single-objective optimization problems, for example, in case of a minimization problem, this value is the decision vector giving the smallest objective that can be achieved within the specified constraints. Hence the minimum decision vector within all possible (feasible) solution vectors is the so-called optimal solution and/or optimal design. However, in multi-objective optimization problems, since a different objective value is generated against each decision vector, the superiority of the solutions over each other is determined by considering the trade-off among the objective values. Therefore, the solution of multi-objective optimization problems, unlike single-objective problems, is a set of vectors rather than a single decision vector. In multi-objective optimization problems, especially if there are intricate objectives, the computational cost of the problem increases. In other words, while synchronously trying to maximize one of the objectives and to minimize another one makes it difficult to find the global optimum design. One of the important techniques used in multi-objective optimization problems is Pareto optimality which enables to select the global optimum solution taking into account the trade-off among all objectives. In this context, using of derivative-based methods has decreased, but the use of metaheuristic methods has increased due to the rapid availability of global optimum solution. This is because the improvements in the field of optimization are progressing in proportion to technology and varying according to the needs. In this chapter, one of the recent metaheuristic optimization methods based on swarm intelligence that is so-called a Pareto-based bat algorithm inspired by the behavior of determining the direction and distance of an object using the echo of the sound called the echolocation of bats is used in order to obtain optimum solutions for multi-objective engineering design problems. In this regard, a four-bar planar truss, a real-sized welded steel beam as well as a multi-layer radar absorber are selected as multi-objective engineering design optimization problems. In case the obtained results (optimal designs) are examined, the potency and the reliability of the proposed multi-objective Pareto-based bat algorithm are demonstrated.

A number of benchmark problems exist for evaluating multi-objective evolutionary algorithms (MOEAs) in the objective space. However, the decision space performance analysis is a recent and relatively less explored topic in evolutionary multi-objective optimization research. Among other implications, such analysis can lead to designing more realistic test problems, gaining better understanding about optimal and robust design areas, and design and evaluation of knowledge-based optimization algorithms. This paper complements the existing research in this area and proposes a new method to generate multi-objective optimization test problems with clustered Pareto sets in hyper-rectangular defined areas of decision space. The test problem is parametrized to control number of decision variables, number and position of optimal areas in the decision space and modality of fitness landscape. Three leading MOEAs, including NSGA-II, NSGA-III, and MOEA/D, are evaluated on a number of problem instances with varying characteristics. A new metric is proposed that measures the performance of algorithms in terms of their coverage of the optimal areas in the decision space. The empirical analysis presented in this research shows that the decision space performance may not necessarily be reflective of the objective space performance and that all algorithms are sensitive to population size parameter for the new test problems.

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Comparison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

This paper is dedicated to the problem of learning finite-state machines (FSMs), which plays a key role in automata-based programming. Metaheuristic algorithms commonly applied to this problem often use FSM mutations (small changes in the FSM structure) for solution construction. Most of them do not employ the specifics of FSMs in their work. We propose a new simple method for improving performance of these algorithms. The basic idea is to mark those transitions of FSMs that were used during fitness evaluation. Then, if a FSM mutation changes a transition that was not used in fitness evaluation, the fitness function value need not be calculated for the mutated FSM. This observation allows to conserve fitness evaluations, which often have high computational costs. The proposed method has been incorporated into several traditional and recent FSM learning algorithms based on evolutionary strategies, genetic algorithms and ant colony optimization. Experimental results are reported showing that the new method significantly improves performance of two methods based on evolutionary strategies and ant colony optimization.

Most of the engineering problems are modeled as evolutionary multiobjective optimization problems, but they always ask for only one best solution, not a set of Pareto optimal solutions. The decision maker′s subjective information plays an important role in choosing the best solution from several Pareto optimal solutions. Generally, the decision‐making processing is implemented after Pareto optimality. In this paper, we attempted to incorporate the decider′s subjective sense with Pareto optimality for chromosomes ranking. A new ranking method based on subjective probability theory was thus proposed in order to explore and comprehend the true nature of the chromosomes on the Pareto optimal front. The properties of the ranking rule were proven, and its transitivity was presented as well. Simulation results compared the performance of the proposed ranking approach with the Pareto‐based ranking method for two multiobjective optimization cases, which demonstrated the effectiveness of the new ranking approach.

Polyploidization events have occurred during the evolution of many fungi, plant, and animal species and are thought to contribute to speciation and tumorigenesis, however little is known about how ploidy level contributes to adaptation at the molecular level. Here we integrate whole genome sequencing, RNA expression analysis, and relative fitness of ∼100 evolved clones at three ploidy levels. Independent haploid, diploid, and tetraploid populations were grown in a low carbon environment for 250 generations. We demonstrate that the key adaptive mutation in the evolved clones is predicted by a gene expression signature of just five genes. All of the adaptive mutations identified encompass a narrow set of genes, however the tetraploid clones gain a broader spectrum of adaptive mutations than haploid or diploid clones. While many of the adaptive mutations occur in genes that encode proteins with known roles in glucose sensing and transport, we discover mutations in genes with no canonical role in carbon utilization (IPT1 and MOT3), as well as identify novel dominant mutations in glucose signal transducers thought to only accumulate recessive mutations in carbon limited environments (MTH1 and RGT1). We conclude that polyploid cells explore more genotypic and phenotypic space than lower ploidy cells. Our study provides strong evidence for the beneficial role of polyploidization events that occur during the evolution of many species and during tumorigenesis.

An Individual-Centered Framework For Unravelling Genotype-Phenotype Interactions

Applications of a similarity measure in the analysis of populations of 3D agents

Evolutionary Optimization based Solution approaches for Many Objective Reliability-Redundancy Allocation Problem

Both evolutionary Bayesian optimization (EBO) and Bayesian evolutionary optimization (BEO) are used to solve time-consuming optimization problems, where in the EBO method, the evolutionary algorithm is adopted to optimize the acquisition function for finding its optimal solution to be evaluated using the time consuming objective functions, while in the BEO approach, surrogates are utilized to replace the expensive objective functions and the acquisition function is used in the model management to choose individuals for evaluations using the expensive objective functions. In this paper, we perform comparisons on these two approaches to see which method is better for solving computationally expensive multi-objective problems. The expected improvement (EI) is used as the acquisition function in both EBO and BEO approaches. Two strategies are proposed to select individuals to be evaluated using the real computationally expensive objectives. The experimental results conducted on ZDT and DTLZ test problems showed that the BEO approach is more efficient than the EBO approach for solving multi-objective problems.

Evolutionary algorithms have been widely used to tackle multi-objective optimization problems. Despite many successful applications there is a lack of theoretical knowledge on how and why this type of algorithm works particularly well for multi-objective problems. This special issue presents current advances to the theoretical understanding of evolutionary algorithms for multi-objective optimization. It comprises four very high quality papers which have been selected via a rigorous reviewing process. The first paper “On the Effect of Populations in Evolutionary Multi-Objective Optimisation” by Oliver Giel and Per Kristian Lehre studies the basic question whether a population is provably useful to compute the whole Pareto front of a multi-objective optimization problem. They compare restart strategies of several single-objective approaches based on one individual to a natural multi-objective approach using a population. Their analyses point out the benefits of the multi-objective evolutionary algorithm in a rigorous way. Using illustrative example functions they provide not only proven results but also a good intuition about why population-based approaches can outperform individual-based approaches in multi-objective optimization. The paper “Exploring the Runtime of an Evolutionary Algorithm for the Multi-Objective Shortest Path Problem” by Christian Horoba examines the behavior of evolutionary algorithms for the classical NP-hard multi-objective shortest path problem. The author considers an evolutionary approach based on -dominance and proves that this algorithm constitutes a fully polynomial-time randomized approximation scheme (FPRAS) for the problem. The algorithm achieves this by mimicking a problemspecific algorithm for that problem. This provides general insight into why evolutionary algorithms can perform well for problems that allow for efficient problem-specific algorithms. Hypervolume-based algorithms have become very popular in evolutionary multiobjective optimization. In the paper, “An Efficient Algorithm for Computing Hypervolume Contributions,” Karl Bringmann and Tobias Friedrich present a faster algorithm for determining the individual with the smallest hypervolume contribution in a given population. Furthermore, they study the problem of removing λ > 1 individuals with the smallest hypervolume contribution from a given population and present an elegant and fast method to carry out this task.

Explainable Interactive Evolutionary Multiobjective Optimization